Jamie Novogrod / NBC News

As her mother, Jean LaFave, looks on, Michele Bachmann signs books at Barnes & Noble in Cedar Rapids, Iowa.

WEST DES MOINES, Iowa -- In a continuing back and forth over Newt Gingrich’s immigration policy, Michele Bachmann criticized the former House speaker Saturday over a letter he co-signed in 2004 in support of President George W. Bush's immigration initiative.

Bachmann's campaign staff handed copies of the letter to the media Saturday morning before an event marking the release of Bachmann's new book, "Core of Conviction," at the Radisson Hotel in Davenport.

“He has a long history of supporting amnesty,” Bachmann told reporters of Gingrich, “and that’s not something that people in Iowa are supporting.”

The letter, originally printed in the Wall Street Journal in February 2004, was sent to the newspaper by the National Foundation for American Policy, a conservative think tank.  Its signers include Gingrich, Jack Kemp, Grover Norquist, and others. Ed Goeas, Bachmann's former campaign pollster, also signed the letter.

Asked by NBC whether Goeas’ signature blunted her attack, Bachmann said, “I did not know him at the time that he signed that letter, nor does he share my opinion.” Goeas left the Bachmann campaign in early October.

The letter supported Bush’s effort to launch a temporary worker program. "We applaud the president and believe his approach holds great promise to reduce illegal immigration and establish a humane, orderly, and economically sensible approach to migration," the letter reads.

Gingrich has taken fire from Bachmann and other candidates, including Mitt Romney and Rick Santorum, since Tuesday's CNN debate in Washington, where he called for a "humane" immigration policy for illegal immigrants "who have children and grandchildren, who are members of the community."

Bachmann’s charge that the policy amounts to "amnesty" is being met with increasingly sharp language by the Gingrich campaign.

"Either Michele Bachmann can't get her facts straight on understanding immigration reform, or she is intentionally lying," Gingrich spokesman R.C. Hammond told NBC News on Saturday while the former speaker was campaigning in Florida.

Gingrich is proposing that longtime illegal residents leave the country and apply for citizenship. He told reporters Saturday he doesn't recall the 2004 letter.

“I have a deep history of supporting efforts to solve the problem of illegal immigration, going back to 1986,” Gingrich told reporters following a book-signing event of his own, citing legislation passed during the Reagan administration.

Despite her attacks, Bachmann spent part of Saturday on the defensive, knocking down comparisons – first noted in Politico and on the conservative website Townhall  –  between Gingrich’s outlook on immigration and remarks she made at the Sept. 7 MSNBC-Politico debate.

At that debate, Bachmann was asked how she would handle the more than 11 million people living in the United States without documentation.  "It depends upon where they live, how long they have been here, if they have a criminal record," Bachmann said.

Asked Saturday how those remarks diverge from Gingrich's position, Bachmann insisted she was speaking about determining which illegal immigrants should be forced to leave the country first. "It is 180 degrees different from where the speaker stands. Because what I'm talking about is order of deportation," Bachmann said.

The book tour Saturday took Bachmann from Davenport, to a Barnes & Noble store in Cedar Rapids, and to a Christian store in West Des Moines.

Bachmann drew about 150 people to each of her second and third stops. But her Davenport visit drew only about a dozen people and will be rescheduled, according to her campaign, which blamed the low turnout on a planning error by the book’s publisher, a conservative imprint of Penguin Books.

Bachmann’s 80-year-old mother joined her at the Cedar Rapids event, beaming as her daughter signed books. Sunday, Bachmann continues her book tour, making stops through northwest Iowa.

NBC's Alex Moe contributed to this report.